Any software connect , whether you notify that or set a recurring schedule, will only verify whether the installed software is in the desired state or not. The desired state is decided by the administrator . The sofwtare will NOT be installed again unless it is found in a broken state or found uninstalled even though the administrator wanted it to be on the client's machine.
The MSI log may not give you a clear picture of what is happening. You can check the actual connect log on the target device,